Non-conservative matrix inequality conditions for stability/stabilizability of linear differential inclusions

作     者：Hu, Tingshu Blanchini, Franco 

作者机构：Univ Massachusetts Dept Elect & Comp Engn Lowell MA 01854 USA Univ Udine Dipartimento Matemat & Informat I-33100 Udine Italy 

出 版 物：《AUTOMATICA》 (自动学)

年 卷 期：2010年第46卷第1期

页      面：190-196页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：NSF [ECS-0621651] Div Of Electrical, Commun & Cyber Sys Directorate For Engineering Funding Source: National Science Foundation 

主　　题：Polyhedral functions Composite quadratic functions Stability Stabilization 

摘      要：This paper shows that the matrix inequality conditions for stability/stabilizability of linear differential inclusions derived from two classes of composite quadratic functions are not conservative. It is established that the existing stability/stabilizability conditions by means of polyhedral functions and based on matrix equalities are equivalent to the matrix inequality conditions. This implies that the composite quadratic functions are universal for robust, possibly constrained, stabilization problems of linear differential inclusions. In particular, a linear differential inclusion is stable (stabilizable with/without constraints) iff it admits a Lyapunov (control Lyapunov) function in these classes. Examples demonstrate that the polyhedral functions can be much more complex than the composite quadratic functions, to confirm the stability/stabilizability of the same system. (C) 2009 Elsevier Ltd. All rights reserved.